UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion Basic Review Energy Budget Physics Behind Heat Pumps Definitions and Terminology 1

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 2 The Energy Budget All bodies emit characteristic energy spectrum Energy Emitted Proportional to Temperature 4 Energy emitted drops as the square of the distance Emission governed by the Stefan-Boltzman Law I = σT 4

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 3 Sun’s Emission Rate 6000°K I = (5.67 x ). ( ) = 73.5 x 10 6 W/m 2 W = (energy per square meter) x (area of photosphere) = (73.5 x 10 6 ) x (4πr 2 ); where r = 647 x 10 6 m = x W Energy Flux: Total Energy:

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 4 Energy Received by Earth W α 1/r 2 r = 150 x 10 9 m A sphere = 4πr 2 = 2.83 x m 2 Energy Flux to Earth: W/m 2 = x Watts / 2.83 x m 2 = 1367 W/m 2 Solar Constant (S o )

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 5 Energy Received by Earth

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 6 Earth’s Disk Energy Received By Earth W = (S o ) (π r 2 ),

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 7 Albedo 30% of incoming radiation is reflected

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 8 Energy Emitted by Earth Short Wave Radiation in Peak λ = 0.47 μm Visible Light Heat Earth Long Wave Radiation out Peak λ = 10 μm Infrared = heat 239 in = 239 out

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 9 Equilibrium Temperature of Earth

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 10 Effects of an Atmosphere

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 11 Effects of an Atmosphere

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 12 Effects of an Atmosphere Equivalent to Equilibrium T of 58°C or 136°F Too Hot!

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 13 Transfer Mechanisms Conduction - transfer of energy by neighboring molecules across a temperature gradient Convection - transfer of energy through larger scale motion of currents – warm air rises, cool air sink – convection Thermals and create weather Latent Heat – transfer of energy through a change in state – evapotranspiration (feeds our weather) Advection – Same as convection but horizontal

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 14

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 15 Energy In = Energy Out The Energy Balance Top of Atmosphere W/m 2 Sunlight Absorbed + IR Back = IR emitted + Thermals + ET (163) (340) (398) (18) (86) Sunlight In = Sunlight reflected (atmos & land) + IR emission (340) (99.5) (239.7) At Earth’s Surface In Atmosphere Sunlight Absorbed + IR Absorb + Thermals + ET = IR space + IR ground (77) (358) (18) (86) (200) (340)

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 16 NASA

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 17 Earth’s Other Energy Source Radioactive decay of three elements 238 U, 232 Th and 40 K produce most of Earth’s internal heat Equivalent to 38 trillion Watts (U.S uses 0.3 trillion Watts) Spread over earth’s surface average heat flow to surface from radioactive decay produces W/m 2 Enough to light a single 75 Watt bulb on 1000 m 2 lot (approximately an area = 100 x 100 ft) Energy absorbed from sun about 2200 times larger than heat flow Davies and Davies, 2010

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 18 The Real World - Insolation NASA

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 19 Long-Wave Radiation Out NASA

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 20 Absorbed Energy NASA

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 21 Average Surface Temperatures NASA

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 22 Temperature Variation with Depth TTeTemperature Variation in °F VT Dept Mines, Mineral & Energy

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 23 Boutt et al., 2010

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 24 Mean Earth Temperatures in U.S. VT Dept Mines, Mineral & Energy

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 25 Energy absorbed by the earth is renewable It is stored by the soil, rock and water GSHP systems borrow this heat temporarily Summary

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 26 Physics of Heat Pumps 1060 Btu to evaporate 1 lb of water (at 60°F) 1060 Btu is released when that 1 lb of water condenses

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 27 Closed system Heat Source (Ground) Heat Distribution (Structure) Expansion Valve Compressor Evaporator Hot Gas, High PressureCool Gas, Low Pressure Hot Liquid, High Pressure Condenser Cooler Liquid/Vapor Mix Low Pressure Heating

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion Ground Exchanger(GHEX) Interior Air Distribution 28 Coupling the Heat Pump Three main components to the System Heat Pump

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 29 GSHP Vocabulary BTU – British Thermal Unit: energy required to raise 1 lb water 1 °F Therm – 1 Therm = 100,000 BTU Ton – 12,000 BTU/h: the amount of heat required to melt 1 ton of ice in 24 hours So, 288,000 BTU to melt 1 ton of ice

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 30 Thermal Conductivity Thermal Conductivity equivalent to Hydraulic Conductivity D constant head reservoir L Sand Darcy’s Experiment (1857) Q   h Q   L Q  A ∆h Q Q  (  h/L) A

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 31 Q/A gradient slope = K = Hydraulic Conductivity Rewrite, Q = Darcy’s Law K  h/L) A For heat flow: Q = heat flow in Btu/hr  h/L = temperature gradient = ∆T/L (°F/ft) A = cross sectional area of flow = L 2 (ft 2 ) K = thermal conductivity = ʎ (Btu/hr/°F/ft)

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 32 Pulling terms together, Q = ʎ (∆T/L) A ʎ = QL/∆TA Units are: Btu/hr/°F/ft 1 Unit Volume 1 1 Conceptually, Temperature Gradient = ʎ = Heat Flow in Btu/hr through a unit length of material per unit area under a unit temperature gradient

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 33 Specific Heat Capacity c p - Specific heat capacity is the amount heat energy a unit mass of material takes into storage or releases from storage per unit change in T 1Btu/lb/°F This is equivalent to specific storage in hydrogeology

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 34 Conceptual Meaning of Specific Heat Capacity 1 unit Mass Earth Heat Out or In 1 unit ∆ in T

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 35 Volumetric Heat Capacity is also equivalent to specific storage s is the amount of heat energy a unit volume of material takes into storage or releases from storage per unit change in T. s has units of Btu/ft 3 /°F s = c p ρ Volumetric Heat Capacity Specific and Volumetric Heat Capacity are related by

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 36 Conceptual Meaning of Volumetric Heat Capacity Heat Capacity 1 unit Volume earth Heat Out or In 1 unit ∆ in T

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 37 Heat Capacity Heat Capacity is equivalent to Storage used in hydrogeology C = ∆Q/ ∆T C = Heat Capacity in Btu/°F ∆Q = heat energy in Btu ∆T = temperature in °F

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 38 Heat Capacity and Specific Heat Capacity Two important relationships: C = c p x total mass of material being heated C = s x total volume of material being heated

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 39 Thermal Diffusivity Thermal Diffusivity equivalent to Transmissivity D = ʎ / c p ρ D is a measure of the rate at which a temperature disturbance at one point in a body travels to another point in the body – similar to transmissivity English Units are: ft 2 /hr Thermal conductivity / volumetric heat capacity

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 40 GSHP Efficiency Terminology Coefficient of Performance – COP energy in or energy output (Btu/h) electrical energy needed (Btu/h) at a specific T Energy Efficiency Ratio – EER (steady state cooling eff.) cooling capacity (BTU/h) electrical energy input (Btu/h) at a specific T Seasonal Energy Efficiency Ratio (SEER) total cooling over entire cooling season (BTU/h) electrical energy used over cooling season (Btu/h) EER = x SEER

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 41 GSHP Acronyms EAT Entering Air Temperature EWTEntering Water Temperature LWTLeaving Water Temperature HCTotal Heating Capacity TCTotal Cooling Capacity CFMCubic Feet per Minute GPMGallons per Minute GSHPGround Source Heat Pump

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 42 Important Conversions & Calculations 1 Watt = 1 Joule/sec 1 Watt = BTU/hr 1 Btu = heat to raise 1 lb of water 1 degree Farenheit 12,000 Btu’s per hour = 1 ton

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion 43 A Useful Calculation Flow (gpm) x T difference (°F) x 500 = Q (Btu/hr) Eg., ((1 gpm x 60 min/hr)/7.481 gal/ft 3 ) x 62.4 lbs/ft 3 = 498 lbs water/hr (~500 lbs/hr) In a closed loop system: for a 10 degree temperature difference 1 gpm x 500 lbs/hr x 10 °F temp diff. = 5000 Btu/hr Therefore, 1 gpm adds 5000 Btu’s of heat per hour 5000 Btu/hr / 12,000 Btu/hr/ton = 0.42 tons or 1 gpm flow needed per 0.42 tons or 2.4 gpm required per ton of heating or cooling when you have a 10° temp. diff.

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion The Thermodynamics of it All: Do GSHPs Work in Cold Climates? Coefficient of Performance (COP) = Heat Energy Output Electric Energy Input Industry claims COP ranging from 3 to 6 From the Second Law of Thermodynamics and the Carnot cycle: COP theoretical limit = Indoor Temperature (Indoor Temperature - Temperature of Heat Source/Sink) 44

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion Thermodynamics (continued) Degrees Farenheit to degrees Kelvin conversion: °K = 5/9 (°F - 32) Example: Heat a dwelling to 70 °F ~ 294 °K Ambient groundwater temperature in Massachusetts is typically about 54 °F ~ 285 °K From the Carnot cycle: COP theoretical limit = 294 °K = °K – 285 °K 45

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion Thermodynamics (continued) What happens to the theoretical efficiency toward the end of the heating season if the entering water temperature has dropped to 35 °F? 35 °F ~ 275 °K COP theoretical limit = 294 °K = °K – 275 °K 46

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion Thermodynamics (continued) Why is the theoretical heat pump efficiency many times greater than the actual COP? No heat pump is 100% efficient - Not all of the energy put into the heat pump is converted into the work of pumping heat – some energy “lost” as waste heat It takes energy to pump the heat transfer fluid through the ground coupled part of the system and the air or water through the building’s heating ducts 47

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion Ground Exchange vs. Air Exchange Heating season Cooling season °F°F

UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept to Completion Entering Heat Pump Temperature vs. Theoretical Maximum COP Entering Temperature ° F Theoretical Coefficient of Performance